Why won't my phone number appear in settings for iMessage

No this has nothing to do with using your email address as a point of contact on your other devices.

To fix your missing phone number issue, turn off iMessage and FaceTime in your settings and then send a text message to a non-iOS person you know, which would be a regular SMS text. Wait a few minutes, and maybe throw in a device reset (not restore) and then re-enable iMessage and FaceTime. This process may register your phone number with the iMessage system, or just the act of resetting the device with iMessage off cures whatever causes this. The reason I suggest turning off FaceTime too is that there seems to be some link between the two services.

If this works, make sure that you have the email associated with your iCloud account also as one of your points of contact, but set your phone number as the "send from". Including your iCloud account's email seems to be required if you want to use SMS relay with your Mac and iDevices, but this would not be required for iMessage itself (i.e. iMessages will always go to your other devices, but SMS can only be routed to them if they're sharing an email address with your iPhone).

Maybe try again, but sign out of everything on all devices -- that means sign completely out of iMessage, FaceTime, and iCloud on your iPhone, iPad, and Mac. Reboot each device, then starting with your iPhone send a couple of SMS messages, and then sign into iCloud and then FaceTime (which also signs you into iMessage). If your iPhone then shows your phone number in your "Start New Conversations From:" then sign into iCloud and FaceTime on your other devices.